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A new maximal subgroup of E8 in characteristic 3
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Cravens, David W., Stewart, David I. and Thomas, Adam (2021) A new maximal subgroup of E8 in characteristic 3. Proceedings of the American Mathematical Society, 150 (4). pp. 1435-1448. doi:10.1090/proc/15759
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Official URL: https://doi.org/10.1090/proc/15759
Abstract
We prove the existence and uniqueness up to conjugacy of a new maximal subgroup of the algebraic group of type E8 in characteristic 3. This has type F4, and was missing from previous lists of maximal subgroups produced by Seitz and Liebeck–Seitz. We also prove a result about the finite group H = 3D4(2), namely that if H embeds in E8 (in any characteristic p) and has two composition factors on the adjoint module then p = 3 and H lies in a conjugate of this new maximal F4 subgroup.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Group theory, Maximal subgroups | ||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||
| Publisher: | American Mathematical Society | ||||||
| ISSN: | 0002-9939 | ||||||
| Official Date: | 2021 | ||||||
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| Volume: | 150 | ||||||
| Number: | 4 | ||||||
| Page Range: | pp. 1435-1448 | ||||||
| DOI: | 10.1090/proc/15759 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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